Give the Berger 185gn BT Juggernaut a try. When it was first around, its designer Bryan Litz was winning long-range sling matches with it in a 30-inch 1 in 13-inch twist barrel, although he noted the twist was too slow, and rebarrelled to a 12-inch twist the following year.
At that time, seven maybe eight years ago, an Sg factor (coefficient of stability) factor of 1.40 was recommended as calculated by the Miller Rules formula. (Theoretically anything above 1.000 is stabilized, but considerably higher values are actually needed.) This is a quick and not too dirty calculator available as an Excel spreadsheet to download if you Google it. You do need the bullet length though - it, the calibre, and the twist rate are the major factors in determining the likely Sg value. (For Berger bullets, go on the company website, click on Ballistics then take the bottom option Twist Rate Calculator. All Berger match bullets are available in its menu and it's very easy to use.)
Weight affects the results too, likewise speed, but less than you think and in fact for any given calibre / bullet length / MV combination the heavier the bullet the higher the Sg and the 'slower; the twist needed. People traditionally talked bullet weights re required twists because as they become heavier in a calibre, they become longer - usually. Nowadays, we have so many very long for weight and calibre bullets around thanks to long-nose designs to reduce drag and increase BC values, weight alone becomes even less reliable as an indicator.
Taking 30 cal and three pairs of bullets in your 12 inch twist barrel:
168gn Sierra MK (1.215" OAL) .......................... 1.72 Sg
168gn Berger Target Hybrid ((1.296" OAL) ......... 1.43 Sg
(assuming 2,700 fps MV)
175gn Sierra MK (1.240" OAL) ................................. 1.67 Sg
175gn Berger Target BT Long Range (1.279" OAL) .... 1.52 Sg
(assuming 2,600 fps MV)
190gn Sierra MK (1.353) .................................. 1.39 Sg
185gn Berger Juggernaut (1.353) ...................... 1.35 Sg
(assuming 2,500 fps MV)
These are all in standard ballistic conditions (59-deg F; 29.92 inches mercury atmospheric pressure). If you shoot in the Arctic in winter on the foreshore, the Sg values are depressed and you may need a 'faster' twist. If you shoot at 7,000 ft ASL (as in Raton NM) in 80 or 90 deg F, the SG values rise considerably and you can 'get away' with a markedly 'slower' twist.
Noe there is another twist (pun!) to the tale. After years and years of ballisticians recommending 1.4 Sg or higher as a target, a couple of years ago, it was raised to 1.5 by Bryan Litz / Berger Bullets. This was because recent research showed that whilst bullets given Sg values above ~1.3 shoot and group fine and appear fully stabilised, they create some extra drag (same effect as reducing the BC) up to 1.5 where everything is now peachy.
So, if you take the 168gn Berger Hybrid in your 12 inch barrel which in give or take conditions is on or just above the old recommended 1.4, go on the Berger twist calculator and it'll tell you it is 'marginally stabilised', and quote the BC loss - 3% is the calculation. So, a bullet with a nominal average G7 BC of 0.269 reduces to an estimated 0.258, still higher than the shorter, blunter Sierra MK's calculated 0.243.
The Juggernaut at 1.35 loses a little more Berger saying it's minus 4% or its nominal G7 value dropping from 0.283 to ~0.272, still a very high BC compared to equivalent competitors.
So, all of the above (and many more) can be used in your barrel, but some will lose a bit of efficiency. Avoid most VLDs and Berger Hybrids weighing more than 168, maybe 175gn as their additional length really drops Sg values and serious stability problems arise. For a cheap, well made and short to mid range bullet, the Sierra 168 and 175 (plus the similar Nosler CC models) will shoot very well in your barrel. For a step up at a bit of hit in your wallet, the 175gn Berger BT Target Long-Range (not same weight Berger VLD) is an easy to tune very well mannered bullet that has a high BC and is fully stabilised in a 12 twist barrel. Also, try the 185gn Juggernaut and see how it works - an excellent bullet for 26-inch barrel rifles for long ranges. It should be OK in summer weather and you'd be able to live with a slight drop in its BC.